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Seminario / Lewis

Il giorno VENERDI' 17 GENNAIO, alle ore 14.00
presso l'Aula Dottorato
del Dipartimento di Matematica (Via Saldini 50),



il Prof. Mark L. LEWIS
(Kent State University, Kent OH)



terrà un seminario dal titolo



"Groups where the centers of the irreducible characters form a chain"



Abstract: Throughout our talk, all groups will be finite. We
consider groups where the centers of the irreducible characters form a
chain. We obtain two alternate characterizations of these groups. One of
these characterizations involves the centers of all quotients of the
group. The other characterization looks at finding a chain of normal
subgroups that have a given problem. We obtain some information
regarding the structure of these groups. In particular, we obtain a
necessary and sufficient condition for a nested group to be nilpotent.
Using our results, we are able to classify those groups where the
kernels of the irreducible characters form a chain. We also classify the
groups where the kernels of the nonlinear irreducible characters form a
chain. This generalizes a result of Qian and Wang that answered a
question that was posed by Berkovich.
A GVZ-group is a group where every irreducible character vanishes off
its center. We consider some alternate definitions of nested groups, and
we show for GVZ-groups, that these different definitions are equivalent.
We present examples that show that these different definitions are not
equivalent for all groups. We show that a result of Nenciu regarding
nested GVZ groups is really a result about nested groups. We give strong
results regarding nested groups that are nilpotent of nilpotence class
2. Finally, we obtain an alternate proof of a theorem of Isaacs
regarding the existence of p-groups with a given set of irreducible
character degrees.



Tutti gli interessati sono invitati a partecipare.

17 gennaio 2020
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